Question

A student is performing the experiment of resonance column. The diameter of the column tube is $6\text{cm}$. The frequency of the tuning fork is $504\text{Hz}$. The speed of the sound at the given temperature is $336\text{m/s}$. The zero of the meter scale coincides with the top end of the resonance column tube. The reading of the water level in the column when the first resonance occurs is -

• A. $13\text{cm}$
• B. $14.8\text{cm}$
• C. $16.6\text{cm}$
• D. $18.4\text{cm}$

Answer 1

The correct option is B $14.8\text{cm}$

Given:
$d=6\text{cm}$
$f=504\text{Hz}$
$v=336\text{m/s}$
$e=0.3d$

So, $\lambda =\frac{v}{f}=\frac{336}{504}=0.6667\text{m}=66.67\text{cm}$

Now,

$l$ $+$ $e$ $=$ $\frac{\lambda }{4}$

$\Rightarrow l$ $+$ $0.3d$ $=$ $\frac{\lambda }{4}$

$\Rightarrow l$ $+$ $0.3\times 6$ $=$ $\frac{66.67}{4}$

$\Rightarrow l=14.87\text{cm}$